Question 25 from the 2010 case study, 2 p.m
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25. Oil is pumped out of an open container using a centrifugal pump; the flow rate is 135 m3/h, the temperature of the fluid is 20°C, and at this temperature the saturated vapor pressure of the oil is 13.6 kPa. The density of the oil is 780 kg/m3. The total length of the suction pipe of the centrifugal pump is 8 m, with an inner diameter of d=125 mm; the friction coefficient of the straight section is λ=0.025, and the overall local resistance coefficient is ∑ξ=2. The local elevation is 1250 m; the NPSHr of this centrifugal pump is 5.5 m, with a safety margin for NPSH taken as 1 m. So, which of the following values is the minimum allowable installation height (m) required for this pump during normal operation? Hint: Atmospheric pressure at different altitudes: Altitude, in meters: 0, 100, 300, 500, 800, 1000, 1500, 2000, 2500. Atmospheric pressure in meters of water column: 10.3, 10.2, 9.95, 9.47, 9.38, 9.16, 8.64, 8.15, 7.65. (A) 1.37, (B) 3.08, (C) -0.68, (D) -8.22. In the answer, the atmospheric pressure is first calculated as (9.106 + 8.64)/2 = 8.9 meters of water column; then it’s not clear how to determine that p0 = 8.85. Does anyone know how to do this? If I just assume that p0 is 8.9 million water columns
Establish an xy coordinate system with atmospheric pressure as the abscissa and altitude as the ordinate, and mark the corresponding values for each data set in the table on this coordinate system. Then, use a smooth curve to connect the various points, and take the air pressure value on that curve at an altitude of 1250. If there’s anything you don’t understand. For exams, I would also simply calculate the average, as the differences between the four options are large enough that such errors can be ignored
What everyone says about drawing is wrong! ! ! Exams don’t allow drawing! And the error is large! Using scientific numerical methods to solve problems is required by the exam syllabus! This method is: Lagrange interpolation! The association’s handouts also cover issues related to numerical methods! Be sure to pay attention! P=9.16+(8.64-9.16)*(1250-1000)/(1500-1000)=8.9 mH2O